Modern notation

Traditional notation starts from a few certainties. The octave has twelve notes, and the smallest distance between two of them is the semitone. Each note has an exact pitch, a place on the staff. And time is measured in beats: a quarter note lasts one beat, a half note two.

In the twentieth century some composers wanted sounds that escaped those certainties: notes between the keys of the piano, chords that are a smear of neighbouring notes, pitches the performer chooses, durations measured by the clock. Writing them down meant inventing signs (Med 1996, ch. LVIII).

Those signs do not form a system. Med regrets that the writing and the reading of the new sounds are not unified worldwide, and that they vary from one composer to another (Med 1996, ch. LVIII). So a score that uses them usually comes with a legend, a page that explains what each sign means in that work. The examples below are the most frequent, not the only ones.

Microtones: notes between the semitones

Microtonal music uses distances smaller than a semitone: a quarter of a tone, an eighth, a twelfth (Med 1996, ch. LVIII). Some cultures use intervals like these often, such as Arab and Indian music. In the West the experiments come from composers such as Ferruccio Busoni, Arnold Schoenberg, Ivan Wyschnegradsky and, above all, the Czech Alois Hába (Med 1996, ch. LVIII).

The quarter tone is the most common microtone. Splitting each of the octave's twelve semitones in half gives 24 notes to the octave, a system Med calls bichromatic music (Med 1996, ch. LVIII). To write it, the accidentals grow variants. Several sets of signs are in use:

• half accidentals: a sharp with a single vertical stroke raises by a quarter tone instead of a whole semitone; a mirrored flat lowers by a quarter tone;
• accidentals with arrows: a sharp, flat or natural with a small arrow up or down, which nudges the note a quarter tone that way.

Hába went further and wrote sixths and twelfths of a tone, with accidentals crossed by extra strokes (Med 1996, ch. LVIII). Reading them takes a trained ear and, often, instruments built for it.

Not every theory book goes there. Blatter acknowledges that microtones exist in the music of other cultures and in some Western composers, and leaves them outside his book (Blatter 2007, part 1, endnote 8). It is a common choice: the twelve-semitone system is still the ground almost all written and taught music stands on.

Clusters: chords of seconds

A traditional chord stacks thirds: C, E, G. A cluster, or tone cluster, stacks seconds, neighbouring notes sounding together. The English word means a heap, a crowd (Med 1996, ch. LVIII), and that is what you hear: a smear of sound instead of a chord with distinct notes.

Compare the C major triad with a cluster of the five white notes from C to G:

Hear the passage

On the piano a cluster is played with the flat of the hand or the forearm. Med distinguishes two kinds (Med 1996, ch. LVIII):

Kind	Notes	How it is written
diatonic cluster	natural notes only, the white keys	a hollow block between the lowest and the highest note
chromatic cluster	natural and altered notes, white and black keys	a filled, black block

Writing the block instead of every note spares the staff a pile of crowded noteheads and tells the pianist at a glance where the cluster starts and ends. In Alban Berg's opera Lulu the piano plays a white-key cluster in the bass clef and a black-key cluster in the treble clef (Med 1996, ch. LVIII).

Pitches the performer chooses

Some signs leave the exact pitch open and give only the region (Med 1996, ch. LVIII):

• an upward arrow leaving the staff asks for the highest possible note on the instrument, and a downward arrow for the lowest;
• a slanting arrow into the staff asks for a note in the middle register;
• a sound line, curved and continuous, draws the contour the pitch should follow, rising and falling;
• a band with an approximate path asks the performer to improvise along that trajectory.

Some composers went further and made a whole notation of their own. Nicolas Obukhov, a Russian composer who settled in Paris, wrote the chromatic notes of his atonal music with cross-shaped signs instead of sharps and flats, a notation Med finds very practical (Med 1996, ch. LVIII).

Time without a meter

Another group of signs deals with duration when there is no beat to count (Med 1996, ch. LVIII):

• a horizontal line after the notehead shows how long the note lasts by its length, like a graph;
• a figure such as 0.30, or 30", marks an approximate duration of thirty seconds;
• beams that multiply into a fan, or vertical strokes drawn closer and closer, ask for an accelerando; the reverse drawing, with beams thinning out and strokes moving apart, asks for a ritardando;
• a beam crossed by a slash asks for the notes to be played as fast as possible;
• a wavy line, a dashed arrow or a zigzag after a figure asks the performer to keep repeating that pattern;
• a black wedge that widens or narrows asks for a crescendo or a decrescendo, in place of the traditional hairpin's two lines.

The shortest possible sound has its own sign too: a note whose flag is crossed by a stroke.

Graphic scores

At the far end, the staff gives way to drawing. Fields of sound points stand for few sounds when the dots are scattered, or many when they are packed; triangles, lines and waves join them and make a score that reads like a map. Wavy lines of different widths ask for different kinds of vibrato (Med 1996, ch. LVIII).

In these scores the legend stops being an appendix and becomes part of the work: without it there is no way to know what to play.

How to read a score like this

1. Look for the legend, on the first page or in the preface. The same sign can mean different things in two composers.
2. Separate what is exact from what is open. A note written on the staff is still that note; an arrow or a band asks for a choice of yours.
3. Read time in seconds where the score asks for it, and only go back to counting beats when the score goes back to having a meter.

Med ends the chapter by recommending further study of notation in contemporary music (Med 1996, ch. LVIII), and the advice is fair: what is shown here are the signs that turn up fairly often, and each new work may bring its own.